"It's a very different world, and having Amazon jump in is not a good sign for existing brands, either branded or private label, because the way Amazon works is its ability to take on unprofitable ventures for a time to see how things go," said Matthew Oster, head of consumer health research at global market research firm Euromonitor International.
"And the fact they have a near monopoly in e-commerce gives them a lot of scale that can allow them to undercut price. So that aspect should be concerning for whoever their competitors are in that space," he said.
An Amazon spokeswoman said Basic Care does not give it a pathway into selling prescription drugs. However, CNBC has reported on the company's interest in the space, including that Amazon has participated in exploratory talks with generic-drug makers. The company announced a partnership with J.P. Morgan and Berkshire Hathaway in January to create a company aimed at reducing health-care costs.
Amazon joined the medical supplies business when it inked a deal with Cardinal Health in 2014, according to a source familiar with the matter. The agreement started with Amazon administering the company store so Cardinal employees could get discounts, and then grew into selling to consumers via Amazon.com, the source said.
Cardinal did not immediately respond to CNBC's request for comment.
Skeptics say the regulatory hurdles in health care may be too high for even the mighty Amazon to overcome. But selling private-label OTC drugs — though less sexy than some alternatives — could be a much easier way to crack into health care.
Private label brands represent 31 percent, or $8.4 billion, of the U.S. OTC medication industry, according to Euromonitor. Still, branded products dominated every category except smoking cessation, according to data from Nielsen, meaning there's plenty of room for private-label drugs to grow.